Which Pokémon game introduced Shiny Pokémon to the series?

Pokémon Gold and Silver introduced Shiny Pokémon to the series.

Released for the Game Boy Color in Japan on November 21, 1999, Gold and Silver formed the second generation of the main Pokémon games. They added 100 new species, bringing the National Pokédex total to 251.

A Shiny Pokémon has an alternate coloration compared with its ordinary appearance. In Gold and Silver, encountering one was exceptionally unlikely, and the games used a brief sparkle animation to emphasize the unusual appearance.

The Red Gyarados encountered at the Lake of Rage provided a guaranteed story encounter with a Shiny Pokémon. This made the new feature visible to virtually every player, rather than leaving it entirely dependent on luck. Shiny status is separate from a Pokémon's species, so a Shiny Pokémon remains the same species with a different color scheme.